Hostname: page-component-cb9f654ff-mnl9s Total loading time: 0 Render date: 2025-09-04T17:11:44.344Z Has data issue: false hasContentIssue false
  • English
  • Français

The dipolar field of rotating bodies in two dimensions

Published online by Cambridge University Press:  30 June 2008

STEFAN G. LLEWELLYN SMITH ,
SÉBASTIEN MICHELIN  and
D. G. CROWDY
STEFAN G. LLEWELLYN SMITH
Affiliation:
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, 9500 Gilman Drive, La Jolla CA 92093-0411, USA
SÉBASTIEN MICHELIN
Affiliation:
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, 9500 Gilman Drive, La Jolla CA 92093-0411, USA École Nationale Supérieure des Mines de Paris, 60–62 Boulevard Saint Michel, 75272 Paris cedex 06, France
D. G. CROWDY
Affiliation:
Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The fluid velocity far from a translating body in two-dimensional irrotational flow is generally dipolar. This is a classical result. Here we ask when the dipolar component vanishes. Lamb (1945, § 126) provides symmetry conditions on the virtual mass tensor for this to be the case. We show that these conditions are not necessary and obtain the sufficient and necessary condition in terms of the shape of the body using conformal maps. Some explicit examples are constructed based on this condition.

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 607 , 25 July 2008 , pp. 109 - 118
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Goodman, A. W. 1983 Univalent Functions. Tampa, Florida: Mariner.Google Scholar
Henrici, P. 1974 Applied and Computational Complex Analysis, vol. 1. Wiley.Google Scholar
Kühnel, W. 2006 Differential Geometry: Curves – Surfaces – Manifolds, 2nd edn. American Mathematial Society.Google Scholar
Lamb, H. 1945 Hydrodynamics, 6th edn. Dover.Google Scholar
Marden, M. 1985 Geometry of Polynomials, 2nd edn. American Mathematical Society.Google Scholar
Newman, J. N. 1977 Marine Hydrodynamics. MIT Press.Google Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar